Ron Aharoni's Mathematics, Poetry and Beauty PDF

By Ron Aharoni

ISBN-10: 9814602949

ISBN-13: 9789814602945

What does arithmetic need to do with poetry? likely, not anything. arithmetic bargains with abstractions whereas poetry with feelings. And but, the 2 proportion anything crucial: good looks. “Euclid on my own has regarded on good looks bare,” says the name of a poem via Edna St. Vincent Millay.

“Mathematics, Poetry and wonder” attempts to unravel the key of the similarity among the 2 domain names. It attempts to provide an explanation for how a mathematical argument and a poem can circulation us within the similar approach. Mathematical and poetic concepts are in comparison, with the purpose of revealing how they evoke an analogous experience of beauty.

The reader may perhaps locate that, as Bertrand Russell stated, “Mathematics, rightly considered, possesses not just fact, yet splendid attractiveness — a good looks carry and austere, like that of sculpture … sublimely natural, and in a position to a stern perfection corresponding to in simple terms the best paintings can show.”

Readership: these attracted to arithmetic, these attracted to poetry, and most people.

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Sample text

Legend has it that, one day Pythagoras was passing by a blacksmith’s workshop, and realized that when the blacksmith struck rods with a simple ratio between their lengths — for example, one was twice as long as the other or one and a half times as long, the combination of the two sounds was pleasing to the ear. In modern terminology, two sounds sound well together if the ratio between their frequencies is simple, that is, it is expressed by small numbers (for example 3:2 is simpler than 11:5). The frequency of a sound is the number of times per second the air vibrates when the sound is produced, or in more precise language: the number of peaks per second of the sound waves.

The cult numbered about 600 men and women, who lived in the Greek colony of Crotona in the south of the Apennine peninsula, in the “heel” of the Italian boot. They donated all their possessions to the community, and swore to keep their discoveries secret. Legend has it that, one day Pythagoras was passing by a blacksmith’s workshop, and realized that when the blacksmith struck rods with a simple ratio between their lengths — for example, one was twice as long as the other or one and a half times as long, the combination of the two sounds was pleasing to the ear.

If this is so, it easily follows that for every ascent (that rises by a factor of about 3), there are, on average, 2 descents. Since these two descents mean going down by a factor of 4, every ascent times 3 is typically matched by a 4 times descent. Therefore, on average, we drop further than we rise, so that, eventually, there is a good probability of reaching 1. Of course this does not constitute a proof, because even if the probability of an event is low, it can still occur. Another difficulty is that the numbers can go in a circle: there is no a priori reason why, say, if we begin with the number 537, the sequence will not eventually come around again to 537, just as when we begin with 1 we return to 1 (the sequence beginning with 1 is: 1, 4, 2, 1).

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Mathematics, Poetry and Beauty by Ron Aharoni


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